past simple vs.present perfect

[Christin]

HI everyone, I need to help with the following message which I wrote. I'm not sure about the use of the right tenses.

Hi Tom,

I’m really sorry but I broke your favourite cup. I wanted to give my dirty plate to dishwasher, but your cup was next to the plate and I threw down the cup. It´s my mistake. I would like to pay it or I will buy to you a new one.

Lucy

Should I write: I' m really sorry but I have broken your favourite cup. I wanted to give....
It has been my mistake, or It's my mistake.

[Joe]

It all depends where you are haha

You want US or UK English?

[Christin]

rather UK english because it was homework and preparation for the english exam

[Joe]

British English

I’m really sorry but I have broken your favourite cup. I wanted to put my dirty plate in the dishwasher, but your cup was next to my plate and I threw down (dropped?) your cup. It was my mistake. I would like to pay for it or I will buy you a new one.

[Christin]

Thank you for the correction! So in US english I could use present perfect,right? Now I understand that if I use past simple in the first sentence,it won't be a mistake as well. But the only thing I don't understand is separating last sentence by a comma (because it's a compound sentence so I would write a comma)=> I would like to pay for it, or I will buy you a new one.

[Joe]

In general US uses past in preference to present perfect:

Did you eat already?

This is common in US but strange in UK.

But the present perfect is also used in US, just less than UK.

A comma might be better.

[Christin]

Ok,thanks for your help!